gdritter repos when-computer / a006229
Typos in 19tet section Getty Ritter 7 years ago
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drafts/microtonal-music.telml less more
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7272 \svgimg{/static/microtonal/third-incomplete.svg}
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74 Well, we've generated our twelve notes, but this looks… well, wrong. For one, there are a few surprisingly empty spaces in the scale: for example, we have the two notes 114.79 and 184.35, which differ by 69.56 cents, but the next note up is 368.70, which differs by 184.35 cents—a gap more than twice as large! For another: recall how when we first generated our Pythagorean scale, we decided to stop generating notes when we got to a note that was comparatively close to the root. However, in the chart above, the last frequency we generated before stopping was 806.96 at cents, which means the next note we were going to generate was going to be at 550.55 cents: not close to the root at all! Let's try to keep applying our approximated fifth a few more times and see how long it takes to get reach a frequency that's comparatively close to the root:
74 Well, we've generated our twelve notes, but this looks… well, wrong. For one, there are a handful of surprising empty spaces in the scale: for example, we have the two notes 114.79 and 184.35, which differ by 69.56 cents, but the next note up is 368.70, which differs by 184.35 cents—a gap more than twice as large! For another: recall how when we first generated our Pythagorean scale, we decided to stop generating notes when we got to a note that was comparatively close to the root. However, in the chart above, the last frequency we generated before stopping was 806.96 at cents, which means the next note we were going to generate was going to be 550.55 cents: not close to the root at all! Let's try to keep applying our approximated fifth a few more times and see how long it takes to get reach a frequency that's comparatively close to the root:
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7676 \svgimg{/static/microtonal/third-complete.svg}
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